Question

The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (4, 1) is a point on the curve?

Answer 1

dy/dx = ??

build and solve.....

Answer 2

I'm not sure how to begin

Answer 3

dy/dx = x / y

separate + solve with boundary condition (4, 1) .....

Answer 4

How do you do the boundary condition?

Answer 5

solve the differential equation first, and then use 4,1 to find the integration constant....

Answer 6

would it be x+y=15

Answer 7

if x + y = 15,
then y = -x + 15
so dy/dx = -1

it cannot be that, then.

do you know how to solve the diff equation?